Two unrelated conditions that I've noticed can lead to dropping the chain off the inner ring.

First, with double chainrings, if the outer limit screw is too tight against the cable tension, the release of that tension can cause the chain to overshoot the small ring. Second, overshifting the small ring is more likely to happen on shifts where the chain is on the smaller (outer) cassette sprockets. The combination of the slacker chain and the extra distance between the chain and the inner plate of the derailleur seem to conspire to make overshifts more likely. Shift to the small ring after you've done most of your downshifting on the cassette. Then upshift on the cassette as you need to.